Related papers: Inversion of noisy Radon transform by SVD based ne…
Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional…
We study imaging with an array of sensors that probes a medium with single frequency electromagnetic waves and records the scattered electric field. The medium is known and homogenous except for some small and penetrable inclusions. The…
Recently, the deep-belief-networks (DBN) based voice activity detection (VAD) has been proposed. It is powerful in fusing the advantages of multiple features, and achieves the state-of-the-art performance. However, the deep layers of the…
This paper may be viewed as a companion paper to [G1]. In that paper, $L^2$ Sobolev estimates derived from a Newton polyhedron-based resolution of singularities method are combined with interpolation arguments to prove $L^p$ to $L^q_s$…
We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a…
The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special…
Using integral transforms to the end of lines detection in images with complex background, makes the detection a hard task needing additional processing to manage the detection. As an integral transform, the Scale Space Radon Transform…
We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
A wavelet-based changepoint method is proposed that determines when the variability of the noise in a sequence of functional profiles goes out-of-control from a known, fixed value. The functional portion of the profiles are allowed to come…
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An…
Signal denoising is a key preprocessing step for many applications, as the performance of a learning task is closely related to the quality of the input data. In this paper, we apply a signal processing based deep neural network…
Dynamic mode decomposition (DMD) is a popular approach to analyzing and modeling fluid flows. In practice, datasets are almost always corrupted to some degree by noise. The vanilla DMD is highly noise-sensitive, which is why many…
A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms.…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
We establish strong uniqueness for a class of degenerate SDEs of weak H{\"o}rmander type under suitable H{\"o}lder regularity conditions for the associated drift term. Our approach relies on the Zvonkin transform which requires to exhibit…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…
We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a…
In this paper the generalized Radon transform over level hypersurfaces of CES-functions of measures supported in positive orthant is studied. A characterization of the generalized Radon transform of nonnegative measures is found. Explicit…